Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites

TL;DR

This paper computes the bulk free energy of the eight vertex model with an odd number of lattice sites, confirming that in the thermodynamic limit, the result matches the even-site case, using a root-based approach.

Contribution

It extends the calculation of the eight vertex model's free energy to odd lattice sizes, demonstrating the equivalence with even sizes in the thermodynamic limit.

Findings

Bulk free energy matches the even-site case in the thermodynamic limit.

Uses Fabricius and McCoy's root equation approach.

Confirms theoretical expectations for odd lattice sizes.

Abstract

We calculate the bulk contribution for the doubly degenerated largest eigenvalue of the transfer matrix of the eight vertex model with an odd number of lattice sites N in the disordered regime using the generic equation for roots proposed by Fabricius and McCoy. We show as expected that in the thermodynamic limit the result coincides with the one in the N even case.